Fitting the Weibull and lognormal log-linear models to accelerated life test data

Persistent Link:
http://hdl.handle.net/10150/284924
Title:
Fitting the Weibull and lognormal log-linear models to accelerated life test data
Author:
Wang, Wendai
Issue Date:
1999
Publisher:
The University of Arizona.
Rights:
Copyright © is held by the author. Digital access to this material is made possible by the University Libraries, University of Arizona. Further transmission, reproduction or presentation (such as public display or performance) of protected items is prohibited except with permission of the author.
Abstract:
Accelerated life tests, in which more than one stress is often involved, have become widely used in today's industries to obtain the time-to-failure and reliability information at normal use conditions. Tests are conducted at higher than normal levels of stresses to shorten the test duration. A physical-statistical model is needed to extrapolate the results from test conditions to usage conditions. The generalized Weibull and lognormal log-linear models, as two general ALT families, cover almost all ALT models which are current in use in reliability engineering for this purpose. However, the development of multiple-stress ALTs has been hindered by the difficulty of performing adequate and satisfactory model fitting. This study presents an extensive research on both point and interval estimates of model parameters. The maximum likelihood estimates (MLE), as the first choice of the point estimate, have preferable statistical properties and well-developed theories. Due to complication of the models and data patterns, a robust and efficient algorithm is essential to successful implementation of the ML estimation. Unfortunately, the current methods get impractical, and no effective and practical approach has been developed yet for the generalized Weibull and lognormal log-linear models. A new approach to obtain ML point estimators of the parameters for both models, which takes advantage of generalized linear model (GLM), has been proposed and extensively studied in this research. The algorithm is generally numerically stable and easily programmed. The superiority is that it does not depend much on the starting values. This proposed method might generate a long-standing method to obtain the MLE for the ALT and other models which have two sets of unknown parameters, one in the mean function and other in the variance function. The likelihood ration confidence intervals have been concluded generally to be the best among the available approximate confidence methods, based on recent researches. The LR confidence bound method is successfully applied to calculate the confidence limits on the reliability under the use conditions in this study. Furthermore, the study has established a general method to calculate the LR ratio confidence limits on a function of unknown parameters. The procedures of point and interval estimates have been developed and their virtues have been demonstrated with several numerical examples of actual accelerated life test data.
Type:
text; Dissertation-Reproduction (electronic)
Keywords:
Engineering, Industrial.; Engineering, Mechanical.; Computer Science.
Degree Name:
Ph.D.
Degree Level:
doctoral
Degree Program:
Graduate College; Aerospace and Mechanical Engineering
Degree Grantor:
University of Arizona
Advisor:
Kececioglu, Dimitri B.

Full metadata record

DC FieldValue Language
dc.language.isoen_USen_US
dc.titleFitting the Weibull and lognormal log-linear models to accelerated life test dataen_US
dc.creatorWang, Wendaien_US
dc.contributor.authorWang, Wendaien_US
dc.date.issued1999en_US
dc.publisherThe University of Arizona.en_US
dc.rightsCopyright © is held by the author. Digital access to this material is made possible by the University Libraries, University of Arizona. Further transmission, reproduction or presentation (such as public display or performance) of protected items is prohibited except with permission of the author.en_US
dc.description.abstractAccelerated life tests, in which more than one stress is often involved, have become widely used in today's industries to obtain the time-to-failure and reliability information at normal use conditions. Tests are conducted at higher than normal levels of stresses to shorten the test duration. A physical-statistical model is needed to extrapolate the results from test conditions to usage conditions. The generalized Weibull and lognormal log-linear models, as two general ALT families, cover almost all ALT models which are current in use in reliability engineering for this purpose. However, the development of multiple-stress ALTs has been hindered by the difficulty of performing adequate and satisfactory model fitting. This study presents an extensive research on both point and interval estimates of model parameters. The maximum likelihood estimates (MLE), as the first choice of the point estimate, have preferable statistical properties and well-developed theories. Due to complication of the models and data patterns, a robust and efficient algorithm is essential to successful implementation of the ML estimation. Unfortunately, the current methods get impractical, and no effective and practical approach has been developed yet for the generalized Weibull and lognormal log-linear models. A new approach to obtain ML point estimators of the parameters for both models, which takes advantage of generalized linear model (GLM), has been proposed and extensively studied in this research. The algorithm is generally numerically stable and easily programmed. The superiority is that it does not depend much on the starting values. This proposed method might generate a long-standing method to obtain the MLE for the ALT and other models which have two sets of unknown parameters, one in the mean function and other in the variance function. The likelihood ration confidence intervals have been concluded generally to be the best among the available approximate confidence methods, based on recent researches. The LR confidence bound method is successfully applied to calculate the confidence limits on the reliability under the use conditions in this study. Furthermore, the study has established a general method to calculate the LR ratio confidence limits on a function of unknown parameters. The procedures of point and interval estimates have been developed and their virtues have been demonstrated with several numerical examples of actual accelerated life test data.en_US
dc.typetexten_US
dc.typeDissertation-Reproduction (electronic)en_US
dc.subjectEngineering, Industrial.en_US
dc.subjectEngineering, Mechanical.en_US
dc.subjectComputer Science.en_US
thesis.degree.namePh.D.en_US
thesis.degree.leveldoctoralen_US
thesis.degree.disciplineGraduate Collegeen_US
thesis.degree.disciplineAerospace and Mechanical Engineeringen_US
thesis.degree.grantorUniversity of Arizonaen_US
dc.contributor.advisorKececioglu, Dimitri B.en_US
dc.identifier.proquest9946811en_US
dc.identifier.bibrecord.b39914562en_US
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